You'll want to use 12 gauge wire for a 20 amp circuit which can be loaded up to 2400 watts of power. But to really help you out a bit more could you let us know the size of the room that you're wanting this lighting in and what the ceiling material is?
If it's already drywalled then you'll want to install remodel type recessed cans and if there insulation in the ceiling then you'll also want these cans to be IC rated. The cheapest fixture is not necessarily what you should want to use. Halo brand recessed cans are an excellent quality fixture and can be bought for a reasonable price at Home Depot.
Be aware that the size of bulb used in these fixtures is limited by the trim piece used. The rating for the bulb will be marked on the label inside the can and also on the trim piece selected. I'd suggest using 65 watt bulbs in the 6" cans and I know most the 4" cans are limited to 50 watts each.
This link will explain the different types of lighting and how they should be used.
http://www.sunlighting.net/info/general_recessed.htm
Since a basement is a dark place and in need of good lighting I would suggest you use the following link to make sure you're installing adequate lighting.
http://www.forteelectric.com/Howtolayoutcans.html
You may want to consider installing 6" recessed cans for your general lighting purposes and installing the smaller 4" cans for accent or task lighting.
I used a combination of General down lighting,(using 65 watt bulbs which are spaced about 4 feet apart), Task lighting (track lighting for over a bar area) and Accent lighting (wall washers to highlight a wall area and fireplace mantel and sconces on the walls)
You should also consider zoning these lights rather than controlling them all from a single switch. This way you only need to light the portion of the basement that you're using and not the entire area. Try to use dimmers on all the lighting and make sure the lighting you use doesn't exceed the wattage rating for the dimmers (which are normally 600 watt max, down rated if more than one dimmer is installed in the same electrical box).
If the ceiling is drwalled then the link below will help you in the details of how to install remodeled type cans
http://www.rd.com/content/openConten...ontentId=17776
If the ceiling is a drop ceiling then you should use new work cans and mount them in the ceiling panels as shown in the link below
http://www.armstrong.com/resclgam/na...icle18424.html
I use the metal fish tapes and have had no problems. There are times though when a more solid fish is needed and then the fiberglass rods come in really handy though you should have no problem using the metal tape for installing lighting.